Stability and Robustness: Reliability in the World of Uncertainty

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Special casesProblemFormulationStability andAccuracyFunctionsObviously, if J = ({1}, {2}, ..., {m}) and B r = ∅ for all r ∈ N m(m coalitions, each coalition has one member, no bans), thenthe concept of J-equilibrium transforms into the well-knowconcept of the Nash equilibrium. On the other hand, ifJ = ({1, 2, ..., m}) and B = (∅) (one coalition that contains allplayers, no bans), then the concept of J-equilibrium transformsinto the well-know concept of the Pareto efficiency or Paretoequilibrium.For the game with matrix C, we denote PE m (C, X) andNE m (C, X) the set of Pareto and Nash equilibria, respectively.Sensitivity Analysis in Game Theory Yury Nikulin - p. 8/29
Original problemProblemFormulationStability andAccuracyFunctionsIt is assumed that the set of strategy profiles X is fixed, i.e wehave coalition and ban profiles J and B fixed, but the originalmatrix of coefficients may vary or be estimated with errors.Moreover, it is assumed that for some originally specifiedmatrix C 0 = {c 0 ij } ∈ Rm×m + we know a J-equilibrium x ∗ whichis an element of the set of all J-equilibria JE(C 0 , X).Sensitivity Analysis in Game Theory Yury Nikulin - p. 9/29
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OutlineThe World of UncertaintyRobu
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Interval UncertaintyOutlineThe Worl
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ExampleOutlineThe World of Uncertai
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Introduction: Sensitivity analysis
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Dealing with uncertainty16/04/2009
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Classical approachKouvelis P. and Y
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Telecommunication and MST16/04/2009
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Multicommodity reformulation formin
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Dual problem16/04/2009 Yury Nikulin
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Interval data and scenariosG = ( E,
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RST problem reformulation as mixedi
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Robust Spanning Tree Problem within
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Example: weak edgesweaknon-weak12-5
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Example: Strong edgesstrong12-553-4
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CPLEX results on complete graphs16/
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Branching strategyNode d with the s
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Lower bound16/04/2009 Yury Nikulin,
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SA: preprocessing, initial solution
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SA: neighborhood search moveCase2.1
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Running time16/04/2009 Yury Nikulin
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SA summary• In spite of SA is gen
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Heuristics for Central Tree Problem
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Distance MeasureThe Central TreePro
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Distance MeasureThe Central TreePro
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Stability and Robustness: Reliability in the World of Uncertainty

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